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Q. 63

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A 2.0 kg ball swings in a vertical circle on the end of an 80-cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is θ = 30­o.a. What is the ball’s speed when θ = 30o­?b. What are the magnitude and direction of the ball’s acceleration when θ = 30o­?

a) Balls speed is 3.85 m /sec

b) Ball's acceleration is 18.496 m/sec2

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Step by Step Solution

Part(a) Step 1 : Given Information

Mass of ball is 2 kg
Length of string = 80 cm =0.8 m Tension in the string = 20 NWhen its angle from the highest point on the circle is θ = 30o­.

Part(a) Step 2: Explanation

The centripetal force acting on a mass m revolving with speed v around a circle of radius r is given by

mv2/r ……………………………….(1)

The centripetal acceleration is given by

v2/r ……………………………….(2)

The tension of the spring at a given angle is and solve for v

Substitute the given value we get

Part(b) Step 1: Given information

Mass of ball is 2 kg
Length of string = 80 cm =0.8 mTension in the string = 20 NWhen its angle from the highest point on the circle is θ = 30o­.

Part(b) Step 2: Explanation

The ball's radial acceleration is calculated as

Substitute the values given

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